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8.9 gal to 174: gal, representing a reasonable rangeof energy transmissions through soils that can beused to calibrate:.both low strain .free-field soilprofiles and thee' strain, dependent modulusdegradations. The objective of the BNL free-field .analysis is to identify the test site soil properties interms. of shear wave velocity using theseismometer recordings from these earthquakes.The methodology -employed in the BNLprobabilistic :, analysis foray site identificationincludes the Monte Carlo process in conjunctionwith equivalent linear convolution; analyses. Therandom variable selected to characterize, the siteprofile is the shear wave velocities in each: soillayer of the site profile. A lognormal distribution isassumed with the standard deviation determined .from available site data and applicable regulatoryrequirements. The':median values, are determinedthrough the Fourier ratio methodwith least squarefitting (Xu; 2001). The convolution analyses wereperformed using the CARES program (Xu, 1993)with the appropriate: soil degradation model. and.the outcrop input motions generated .from the...recorded in-column rock' motions. The BNLanalysis produced results . in terms of the mean,'median and various fractiles' of: free-field.: soil;properties. at the test site, and the corresponding.surface response spectra. In this paper, the methodand :procedure-. employed to perform :, theprobabilistic site analysis are,: described first,followed by the results of the BNL analysis with,thirty. randomly sampled profiles generated fromone earthquake motion recorded at the .NUPEC.site.ANALYSIS APPROACH' ,Conventional 'probabilistic analysis consists ofsteps, including:.. .1) identification of randomvariables and' their associated' distributions; 2)modeling. of probabilistic :process for, developing '.various statistical data which ' characterize, the,random variables. under " consideration;'. 3)assessment 'of uncertainties associated with ;the:quantification of the random: variables. In the siteidentification analysis,: soil properties such as unitweight, damping, shear wave velocity (V,) and the "thickness of soil .layers all have inherentrandomness in their measurements, and thereforecould all be selected as random variables.- Theprobabilistic -process established based on all soilproperties and the associated uncertainties .could..be rather complicated and requires significant ,effort to simulate. However, since the SSI effect isprimarily influenced by the shear. wave velocity of '.soils, BNL selected V, to be the random variable

in order to simply :the analysis. The measurementof the other properties could be improved through.the application 'of better techniques andinstruments. The soil: damping is characterizedthrough the GEI modulus;degradation model (GEI,1983), which has been established to be 'suitable..for the NUPEC test site...The BNL analysis assumes . a lognormaldistributions. for V. The probability densityfunction . (PDF) of V,, therefore, assumes , thefollowing form:f = 1 2n v -n v,,,,dv, (v, exp L(1)where vsmed represents .the median estimate of VSand: p is : the. lognormal standard' deviation of .Vscharacterizing:, the uncertainty" for 'the vsmedestimate. The..low-strain vsmed is determined usingthe Fourier ratio .method with. a non-linear. leastsquare fitting. technique. for 'correlating theanalytical site amplification with the amplificationcomputed using the recorded . seismometer, data.The BNL' estimate (Xu, 2001) of the low strainvsmed is shown inFigure 2. .The lognormal standarddeviation is determined using the guidelines of thecurrent version '(NUREG-0800) of the USNRCStandard ' Review Plan. (SRP). The SRPrecommends that the 1.5G and G/1.5 variations :be-used.in SSI'analyses to account for the free fieldsoil uncertainties. Where,. G represents the bestestimate of the shear modules of soils. The rangeof uncertainties determined by 1.5G and G/1.5 is:about the 15th to 85th, percentiles, correspondingto the mean+3 and mean-p estimates. With the aidof the relation::V, = (G/p)'2, and the followingequation:

,# =.In v-. ,

(2)

the lognormal standard deviation p for -V. is.readily calculated to be 0.2.In order to apply-the Monte Carlo method,'randomsampling of the low strain Vs of the free fieldprofile needs be performed.. This is done by usingthe. uniform, distribution for. sampling and the